Abstract
Philosophers, logicians, linguists and even mathematicians have tried to decipher the mechanisms by which concepts are constructed from the meaning of words. One way to achieve this was the study of lexical meaning and its combinatorial properties. Our purpose is to explore the seminal ideas that have resulted in categorial grammars and their relationship with other grammatical models and actual theories of meaning, in a historical process that takes us from the notion of category to that of predication, and from this to the notion of function, then to functional categories and finally to the linguistic notion of argument structure.
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- 1.
Functional and morphosyntactic categories that reach the Roman grammarians—and from them the early modern period—are those proposed by the Alexandrian, who in turn adapted the categories proposed by the Stoic school. The Stoics used a semantic criterion for the classification of the parts of speech, following the Aristotelian style, but they introduced functional changes based on the morphology of words. So, they made a distinction in Aristotle’s syndesmoi between a group of words with inflection that they called arthra (pronouns and articles), and the invariable words (prepositions and conjunctions); they also created the category of adverbs (mesotes) based on syntactic criteria—adverbs appear combined with the verb—as well as morphological ones—adverbs are formed on nominal or adjectival themes and roots. Finally, Stoics introduced the concept of klisis to denote the grammatical variation of a word, limiting the aristotelian notion of case (ptosis) to the words of nominal category (proper names, common nouns and adjectives) as well as to the words classified as arthra (pronouns and articles), this being the basis for the distinction between these categories and verbs (rhema). A more extensive description of the topic can be found at Robins (1969).
- 2.
Among them we can highlight Martin of Dacia, Michel de Marbais, Peter Helias and Thomas of Erfurt. The philosophy of the Modistae drank directly from the work of Aristotle, but also had the probable influence of commentators such as Duns Scotus. Their theories were also clearly related to those of other philosophers of the period as Roger Bacon or William of Ockham.
- 3.
Leibniz’s proposal was very important and influential on the search for universal languages during the eighteenth Century, as well as were his etymological studies on the rise of comparative linguistics at the nineteenth Century.
- 4.
Although this principle is traditionally attributed to Frege, was not he who formulated it, but Rudolf Carnap, who ascribed him the following principles of interchangeability: “First principle […] the nominatum of the whole expression is a function of the nominata of the names occurring in it. […] Second principle […] the sense of the whole expression is a function of the senses of the names occurring in it.” (Carnap 1947: 121). Later, Donald Davidson spread the idea that the Principle of Compositionality is due to the distinction between meaning and reference in Frege: “If we want a theory that gives us the meaning (as distinct from reference) of each sentence, we must start with the meaning (as distinct from reference) of the parts. Up to now we have been following Frege’s footsteps; thanks to him the path is well known and even well worn.” (Davidson 1967: 306).
- 5.
This is the real Frege’s Principle, which was set by him in The Foundations of Arithmetic: “Mann muss die Wörter im Sätze betrachten, wenn man nach ihrer Bedeutung fragt […] Es genügt, wenn der Satz als Ganzes einen Sinn hat; dadurch erhalten auch seine Teile ihren Inhalt.” (Frege 1884: secc. 60).
- 6.
Frege’s idea of replacing the subject-predicate structure by the function-argument structure as a representation of the enunciative sentence was fundamental to the development of the theory of types and Russell’s proposal of a hierarchy of types to solve the so-called Frege’s paradox. Russell’s theory of types influenced Lesniewski’s grammar of semantic categories, but it was more appropriate for formal languages than for natural languages. However, it was Husserl’s theory of a pure grammar which served as a model for Ajdukiewicz’s notion of a logical syntax of natural language because of its more natural conception of semantic categories.
- 7.
In linguistics, the function of adjectives in a Noun Phrase can be interpreted as a restriction of the reference of the nouns they modify, whereas determiners select a subset of the reference of nouns.
- 8.
The correspondence between sentence constituents in a phrase structure grammar and the categorial types proposed by Montague can be easily established from the syntactic functions and the generic meaning attributed to the different parts of speech (Montague 1973/1974: 249–250).
- 9.
The relationship between predicates and arguments depends on the valence of the latter. It was first expressed by the French linguist Lucien Tesnière, for whom an argument is an expression that helps complete the meaning of the predicate (Tesnière 1959[1965]: 128).
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Acknowledgements
This paper is part of the research project “Awareness, Logic and Computation”, financed by the Government of Spain. I would also like to acknowledge all the help and support of the members of the Research Group on Logic, Language and Information at the University of Seville (GILLIUS), as well as the suggestions of an anonymous referee that have been very helpful to improve the original text.
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Salguero-Lamillar, F.J. (2016). The Quest for the Concept in the Twentieth Century: Predicates, Functions, Categories and Argument Structure. In: Redmond, J., Pombo Martins, O., Nepomuceno Fernández, Á. (eds) Epistemology, Knowledge and the Impact of Interaction. Logic, Epistemology, and the Unity of Science, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-26506-3_16
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